In New York State, a Medicaid applicant may transfer the homestead, without penalty, to his/her adult child who RESIDED in the Medicaid applicant's home for at least 2 years, immediately prior to the applicant's most recent institutionalization, and who provided care to the applicant which permitted the applicant to reside at home rather than in a medical facility. It is presumed that the child “provided care” unless there is evidence to the contrary.
Residency is based on the intent to establish a permanent home. Many factors may be considered in asserting residence. Based on a cursory review of the limited information in this question, it appears that it may be difficult to establish that the caretaker child resided in the applicant's home.
You should speak to a qualified elder law attorney before making an application for Medicaid or transferring any assets. Medicaid eligibility is a very complex area of the law and many different factors affect Medicaid eligibility.